Donald Duck Math Puzzle

Mind Teasers :
Donald Duck Math Puzzle

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Donald duck can can swim his pool downstream(with the pool current helping time) in exact 40 seconds and upstream(against the pool current) in a pool in exact 60 seconds. The length of pool is 2 kilometers.

How long Donald duck can cover distance of one side at a still pool (with no current).

* They have only one torch and the river is too risky to cross without the torch.
* If all people cross simultaneously then torch light wont be sufficient.
* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.

What is the shortest time needed for all four of them to cross the river ?

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules

You trade apples from a village to your town. The distance is 1000 miles. This time you were able to get your hands on 3000 apples. You have a truck that can carry just 1000 apples at one time. At every mile is located a check post at which you have to submit 1 apple while going to the town. However, when you travel from town to village, you don’t have to give anything.

How will you make sure that you are able to transport maximum amount of apples to the town?

A thief was running from the police after the biggest theft the town saw. He took his guard in one of the thirteen caves arranged in a circle. Each day, the thief moves either to the adjacent cave or stay in the same cave. Two cops goes there daily and have enough time to enter any two of the caves out of them.

How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?

In the given picture, you can find a few numbers. Now you have to fill each square of the grid in a manner that every row and every column contains the digits 1 to 6. Another thing to keep in mind is that the connected squares must have the same number in them.